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Award ID contains: 1810893

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  1. ; ; (, Studia Scientiarum Mathematicarum Hungarica)
    Extending work of Saneblidze–Umble and others, we use diagonals for the associahedron and multiplihedron to define tensor products of𝐴∞-algebras, modules, algebra homomorphisms, and module morphisms, as well as to define a bimodule analogue of twisted complexes (typeDDstructures, in the language of bordered Heegaard Floer homology) and their one- and two-sided tensor products. We then give analogous definitions for 1-parameter deformations of𝐴∞-algebras; this involves another collection of complexes. These constructions are relevant to bordered Heegaard Floer homology. 
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    Free, publicly-accessible full text available September 18, 2026
  2. ; (, Proceedings of Symposia in Pure Mathematics)
    Feehan, Paul; Ng, Lenhard; Ozsváth, Peter (Ed.)
    Accepted Manuscript Full Text Available
  3. ; (, Bulletin of the American Mathematical Society)
    This is a brief review of the categorification of the Jones polynomial and its significance and ramifications in geometry, algebra, and low-dimensional topology. 
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  4. (, Algebraic & Geometric Topology)
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  5. ; (, Transactions of the American Mathematical Society)
    We construct a mixed invariant of nonorientable surfaces from the Lee and Bar-Natan deformations of Khovanov homology and use it to distinguish pairs of surfaces bounded by the same knot, including some exotic examples. 
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    Full Text Available 
  6. ; (, American Journal of Mathematics)
    Full Text Available 
  7. ; ; (, Journal of Topology)
  8. ; ; (, Documenta Mathematica)
    Full Text Available 
  9. (, Algebraic & Geometric Topology)
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  10. (, Open Book Series)
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